1. Field of the Invention
This invention relates generally to sonic well logging. More particularly, this invention relates to sonic well logging techniques useful in quantifying subsurface parameters which are helpful in searching for and exploiting hydrocarbons and other valuable resources. The invention has particular application to determining dipole flexural dispersion curves as well as shear slowness of a formation via utilization and processing of dispersive wave information such as flexural waves.
2. State of the Art
Sonic well logs are typically derived from tools suspended in a mud-filled borehole by a cable. The tools typically include a sonic source (transmitter) and a plurality of receivers which are spaced apart by several inches or feet. Typically, a sonic signal is transmitted from one longitudinal end of the tool and received at the other, and measurements are made every few inches as the tool is slowly drawn up the borehole. The sonic signal from the transmitter or source enters the formation adjacent the borehole, and the arrival times and perhaps other characteristics of the receiver responses are used to find formation parameters. In most formations, the sonic speeds in the tool and in the drilling mud are less than in the formation. In this situation, the compressional (P-wave), shear (S-wave) and Stoneley arrivals and waves are detected by the receivers and are processed. Sometimes, the sonic speed in the formation is slower than the drilling mud; i.e., the formation is a “slow” formation. In this situation, there is no refraction path available for the shear waves, and the shear waves are typically not measurable at the receivers. However, the shear slowness of the formation is still a desirable formation parameter to obtain.
One sonic log of the art which has proved to be useful is the slowness-time coherence (STC) log. Details of the techniques utilized in producing an STC log are described in U.S. Pat. No. 4,594,691 to Kimball et al., as well as in Kimball, et al., “Semblance Processing of Borehole Acoustic Array Data”; Geophysics, Vol. 49, No. 3, (March 1984) pp. 274–281 which are hereby incorporated by reference in their entireties herein. Briefly, the slowness-time coherence log utilizes the compressional, shear, and Stoneley waves detected by the receivers. A set of time windows is applied to the received waveforms with the window positions determined by two parameters: the assumed arrival time at the first receiver, and an assumed slowness. For a range of values of arrival time and slowness, a scalar semblance is computed for the windowed waveform segments by backpropagating and stacking the waveforms and comparing the stacked energies to the unstacked energies. The semblance may be plotted as a contour plot with slowness and arrival times as axes, with maximum semblance values indicating the determined formation slowness value. In addition, local maxima of the semblance function are identified by a peak-finding algorithm, and the corresponding slowness values may be plotted as gray-scale marks on a graph whose axes are slowness and borehole depth. The intensity of the gray-scale marks is proportional to the height of the semblance peak.
As indicated in the aforementioned article and U.S. Pat. No. 4,594,691 to Kimball et al., the same backpropagation and stacking techniques are used regardless of whether the wave being analyzed is a P-wave, S-wave or a Stoneley wave; i.e., regardless of whether the wave is non-dispersive (P- or S-wave) or dispersive (e.g., Stoneley). However, while such backpropagation and stacking techniques may be optimal for non-dispersive waves, they are not optimal for dispersive waves. In response to this problem, several different approaches have been utilized. A first approach, such as disclosed in Esmersoy et al., “P and SV Inversion from Multicomponent Offset VSPs”, Geophysics, Vol. 55; (1990) utilizes parametric inversion of the total waveform. However, this approach is not preferred because it is unreliable and computationally time consuming.
A second approach which was used commercially is disclosed in A. R. Harrison, et al., “Acquisition and Analysis of Sonic Waveforms From a Borehole Monopole and Dipole Source . . . ”, SPE 20557, pp. 267–282, (Society of Petroleum Engineers, Inc. 1990), which is hereby incorporated by reference herein in its entirety. In the Harrison disclosure, the flexural waveform is processed as in the STC technique, but the non-dispersive processing results is corrected by a factor relating to the measured slowness; i.e., the STC results are post-processed. In particular, correction values are obtained by processing model waveforms with the STC techniques and comparing the measured slowness with the formation shear slowness of the model. The model waveforms assume a particular source and are bandlimited to a prescribed band (typically 1 to 3 KHz) before STC processing. Tables of corrections are designated by a particular source and processing bandwidth, and contain corrections as percentage-of-measured-value factors functions of measured value and hole diameter. The percentage correction required decreases with hole diameter and increasing formation slowness, and ranges from less than one percent to as much as fifteen percent. This approach, as did the parametric inversion approach, has its own drawbacks. In particular, the waveform spectra often disagree with those of the model. Further, the analysis band may exclude the majority of the flexural mode energy as well as reducing sensitivity to environmental parameters.
Other approaches such as first motion detection of flexural mode onset, and non-dispersive processing over a low frequency band, have also been utilized. Each of these approaches, however, has its own drawbacks. The flexural mode onset approach is driven by the realization that the fastest parts of the flexural mode dispersion curve approaches the formation shear slowness, and that the calculated moveout can be taken as the estimate of formation shear slowness. Problems with this technique include, among others, that: the flexural mode onset can be preceded by the compressional arrival; the early onset of the flexural wave may not propagate at the formation shear slowness because the flexural wave does not have energy at low frequencies; early time portions of arrivals have low energy content; measured flexural mode onsets practically never line up exactly in arrays with several receivers. The non-dispersive processing over a low frequency band approach is driven by the realization that the low frequency limit of the flexural mode dispersion curve is the formation shear slowness. Among the problems with the low frequency processing are that: with fixed array lengths, the resolution of the slowness measurement diminishes with frequency; generating significant flexural mode energy at low frequencies is extremely difficult; and road noise increases as the frequency decreases.
In U.S. Pat. No. 5,278,805 to Kimball, which is hereby incorporated by reference herein in its entirety, many of the issues with the previous techniques were resolved. The technique proposed by Kimball in the '805 patent is called dispersive STC or DSTC and has become commercially successful. According to the DSTC technique, a sonic tool is used to detect dispersive waves such as flexural or Stoneley waves. The signals obtained by the sonic tool are then Fourier transformed and backpropagated according to equations using different dispersion curves. The backpropagated signals are then stacked, and semblances are found in order to choose a dispersion curve of maximum semblance, thereby identifying the shear slowness of the formation. Formation shear slowness can then be plotted as a function of borehole depth.
In the Kimball patent, different embodiments are set forth. In one embodiment called quick DSTC or QDSTC, prior to Fourier transforming, the signals are stacked according to a previous estimation of slowness, and are windowed for maximum energy. The reduced set of data in the window are then extracted for Fourier transformation, and prior to backpropagation, multiplied by the estimation of slowness to reset them for backpropagation and stacking. In the standard DSTC embodiment, after the signals are backpropagated, the backpropagated signals are inverse Fourier transformed and windowed. In DSTC, semblance values may be plotted as a function of slowness and time. Regardless of embodiment, Kimball accounts for non-dispersive waves by using dispersion curves of constant value during backpropagation.
While DSTC represented a major improvement in the art, it has since been found by the present inventor that DSTC is not fully accurate. In particular, DSTC employs an assumption that the formation is homogeneous and isotropic, and thus the dispersion curves utilized by the backpropagation technique do not necessarily approximate the dispersion curve of the formation. Thus, when formations deviate from the isotropic, homogeneous formation assumption, the results generated by DSTC are not as accurate as desired.